Results 11 to 20 of about 488,333 (270)

The local limit theorem of Delange in the Knopfmacher's semigroup

Lietuvos Matematikos Rinkinys, 2004
An asymptotic formula of the mean value of multiplicative arithmetic function from the class Ma(G)  with asymptotical expansion of the main term is obtained. In the present paper the local limit theorem of the H. Delange type is proved.
Rimantas Skrabutėnas
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New properties of arithmetic functions related to gcd and lcm [PDF]

Notes on Number Theory and Discrete Mathematics
This paper explores additional properties of the arithmetic functions f_α(n) and g_α(n), defined respectively by f_α(n)=Πʳᵢ₌₁pᵢ^{(eᵢ,α)} and g_α(n)=Πʳᵢ₌₁pᵢ^{[eᵢ,α]}, where n=Πʳᵢ₌₁pᵢ^eᵢ is the prime factorization of a positive integer n>1, (a,b) and [a,b]
Brahim Mittou
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Differentiability of the arithmetic volume function [PDF]

, 2008
We introduce the positive intersection product in Arakelov geometry and prove that the arithmetic volume function is continuously differentiable. As applications, we compute the distribution function of the asymptotic measure of a Hermitian line bundle ...
Chen, Huayi
core   +4 more sources

On a certain class of arithmetic functions [PDF]

Mathematica Bohemica, 2017
A homothetic arithmetic function of ratio $K$ is a function $f \mathbb{N}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in\mathbb{N}$. Periodic arithmetic funtions are always homothetic, while the converse is not true in general.
Antonio M. Oller-Marcén
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New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility

Axioms, 2023
The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms.
Hsien-Chung Wu
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Computation Over Gaussian Networks With Orthogonal Components [PDF]

, 2013
Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function.
Chien-yi Wang, Michael Gastpar, Sang-woon Jeon, Student Member   +3 more
core   +2 more sources

The arithmetic derivative and Leibniz-additive functions [PDF]

, 2018
An arithmetic function $f$ is Leibniz-additive if there is a completely multiplicative function $h_f$, i.e., $h_f(1)=1$ and $h_f(mn)=h_f(m)h_f(n)$ for all positive integers $m$ and $n$, satisfying $$ f(mn)=f(m)h_f(n)+f(n)h_f(m) $$ for all positive ...
Haukkanen, Pentti, Merikoski, Jorma K., Tossavainen, Timo   +2 more
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Two arithmetic functions related to Euler's and Dedekind's functions [PDF]

Notes on Number Theory and Discrete Mathematics
Two new arithmetic functions are introduced. In some sense, they are modifications of Euler's and Dedekind's functions. Some properties of the new functions are studied.
Krassimir Atanassov
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Multidimensional local theorem in the Knopfmachers semigroup

Lietuvos Matematikos Rinkinys, 2007
In the presentpaper a multidimensionallocal theorem for arithmetic functions definedin the Knopfmachers semigroup G is obtained.
Rimantas Skrabutėnas
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The mean value of the function d(n)/d*(n) in arithmetic progressions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
Let d(n) and d*(n) be, respectively, the number of divisors and the number of unitary divisors of an integer n≥1. A divisor d of an integer is to be said unitary if it is prime over n/d.
Ouarda Bouakkaz, Abdallah Derbal
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